Yes. "いろいろ" is used as adverb or noun. So, you can use "いろいろを買います", but I feel this sentence is something like a bit literary... old fashioned... pretentious... affected... I can't find appropriate English words I want to say. Anyway, I think it is not very common in modern conversation.

No, いろいろ, or 色々, literally means "many colors" or "many variations" so it loosely means "various" in English. It does not mean "more than one" in the sense of "i bought more than one thing", by qualifying some quantity, at all. It means I bought various things. "I bought more than one thing" does not imply variety like 色々 truly does, for instance 色々お土産を買った would mean something like "i bought a variety of souvenirs" and not "i bought many souvenirs" which would use 多く, or おおく、instead of 色々.
For quantity, 多く is used to descibe many or a lot of. They are separate words in English- Japanese is no different

I wrote something along the lines of, "I buy many different things." Is that incorrect?
I think this is a hard one to correct because you can express it many ways in English. There's not one way to say it.